Factoring formulas

Below are some factoring formulas that are used to factor some common math expressions.

Factoring formulas trick

Trick to factor aⁿ - bⁿ when n is an odd number. You cannot use this trick if n is even or to factor aⁿ + bⁿ


First start by writing ( a - b ) × ( .................................................. )


Then, fill in the parenthesis on the right.

To do this, follow this guideline.

Subtract 1 from n. For example, if n = 7 as in a⁷ - b⁷, subtract 1 from 7 to get 6.

The first term is always going to be the first variable that is a raised to the power of 6.

The last term is always going to be the second variable that is b raised to the power of 6.

The operation inside is always a plus.

So it is going to look like ( a - b ) × (a⁶ + .................................................. + b⁶)

Now here is the real tricky part!

To get the next term, is a⁵b. This is done by subtracting 1 from 6 and incorporating the other variable.

Now all you have to do is to keep subtracting 1 to the exponent of a and adding 1 to the exponent of b as shown below.

The next term will be a⁴b².

Do this until the variable a disappears and you will end up with the answer already shown above.

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